Kształtowanie rurociągu o zmiennej średnicy, wykazującego pełne uplastycznienie w stadium zniszczenia

In the paper is discussed the design of a pipe line with diameter varying along its horizontal axis subject to variable internal pressure. The pressure changes according to Bernoulli's theorem for ideal liquids. The criterion of full yielding satisfying the plasticity condition (2.4) is used for the optimization of the pipe line form. In the method used the components of stress, strain and the functions a(z) and b(z) are expanded into series of a small parameter. The boundary conditions of the first approximation (3.7) and (3.8) yield the system of homogeneous equations for the constants of integration. The condition of existence of non-trivial solutions determines the form of the body. Sec. 4 presents the full set of formulae derived and a numerical example.